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Hansen, Mowen, Elias & Senkow (ITP, 1998) Chapter 3 - Activity Cost Behaviour Chapter 3-1 Hansen, Mowen, Elias & Senkow (ITP, 1998) Learning Objectives Define and describe cost behaviour and explain the role of the resource usage model in understanding cost behaviour. Separate mixed costs into their fixed and variable components using the high-low method, the scatterplot method, and the method of least squares. Evaluate the reliability of a cost equation. Explain the role of multiple regression in assessing cost behaviour. Describe the use of managerial judgement in determining cost behaviour. Chapter 3-2 Hansen, Mowen, Elias & Senkow (ITP, 1998) Basic Terms - 1 Activity capacity: the ability to perform activities Practical capacity: the efficient level of activity performance Resources: economic inputs that are consumed in performing activities Resource spending: the cost of acquiring capacity to perform an activity Resource usage: the amount of activity capacity used in producing the activity output Chapter 3-3 Hansen, Mowen, Elias & Senkow (ITP, 1998) Basic Terms - 2 Resources supplied as used and needed: these are resources that are acquired from outside sources, where the terms of acquisition do not require any long-term commitment for any given amount of the resource. Examples: materials & energy Resources supplied in advance of usage: these are resources acquired by the use of either an explicit or implicit contract to obtain a given quantity of resource, regardless of whether the quantity of the resource available is fully used or not. Chapter 3-4 Hansen, Mowen, Elias & Senkow (ITP, 1998) Cost Behaviour Fixed Costs Behaviour Variable Cost Behaviour $ $ Relevant Range Activity Activity Unit Cost Varies with Volume Unit Cost Rate is Constant Chapter 3-5 Hansen, Mowen, Elias & Senkow (ITP, 1998) Total versus Average Variable Cost Example: Suppose that Porter Pottery Company makes mugs. Each mug requires 1/4kg. of clay at $2 per kg. If Porter manufactures 5,000 mugs, the total cost of clay is $2,500 (5,000 x $2 x .25). If Porter manufactures 10,000 mugs, total cost of clay is $5,000 (10,000 x $2 x .25). The average cost of clay per mug stays at $0.50 (.25 x 2) no matter how many mugs are made. Chapter 3-6 Hansen, Mowen, Elias & Senkow (ITP, 1998) Total versus Average Variable Cost Total Variable Cost Cost TVC = $.5X $5,000 $2,500 5,000 10,000 Mugs Chapter 3-7 Hansen, Mowen, Elias & Senkow (ITP, 1998) Total versus Average Variable Cost (continued) Average Variable Cost Cost $0.50 AVC = $0.50 5,000 10,000 Mugs Chapter 3-8 Hansen, Mowen, Elias & Senkow (ITP, 1998) Total Fixed versus Average Fixed Cost Total Fixed Cost Cost $1,500 Year 2 $1,000 Year 1 $500 Activity Level Chapter 3-9 Hansen, Mowen, Elias & Senkow (ITP, 1998) Total Fixed versus Average Fixed Cost (continued) Total versus Average Fixed Cost Cost TFC AFC Activity Level Chapter 3-10 Hansen, Mowen, Elias & Senkow (ITP, 1998) The Behaviour of Mixed Costs Linearity Assumption Total Costs $Cost Fixed Costs Variable Costs Number of Units Produced Total Costs = Fixed Amount + Variable Cost Per Unit x Number of Units = Fixed Costs + Variable Costs Y = F + V(X) Y= Total mixed costs (the dependent variable) (X) = Cost Driver or Independent Variable Chapter 3-11 Hansen, Mowen, Elias & Senkow (ITP, 1998) Step Variable Costs Linearity Assumption Narrow Width $Cost Number of Units Produced Chapter 3-12 Hansen, Mowen, Elias & Senkow (ITP, 1998) Types of Fixed Costs Committed Fixed Costs Discretionary Fixed Costs Step Fixed Costs Chapter 3-13 Hansen, Mowen, Elias & Senkow (ITP, 1998) Step Fixed Costs Linearity Assumption $Cost Normal Operating Range (Relevant Range) Number of Units Produced Chapter 3-14 Hansen, Mowen, Elias & Senkow (ITP, 1998) Methods for Separating Mixed Cost Into Fixed and Variable Components The High-Low Method Scatterplot Method The Method of Least Squares Chapter 3-15 Hansen, Mowen, Elias & Senkow (ITP, 1998) Mixed Costs: An Example Month Utility Costs Unit Produced January $2,000 200 February 2,500 400 March 4,500 600 April 5,000 800 May 7,500 1,000 Chapter 3-16 Hansen, Mowen, Elias & Senkow (ITP, 1998) The High-Low Method Variable Cost Rate = (Y2 - Y1)/(X2 - X1) = ($7,500-$2,000)/(1,000-200) = $5,500/800 = $6.875 per unit Fixed Costs = Y2 - VX2 = $7,500 - ($6.875 x 1,000) = $625 The cost formula using the high-low method is: Y = $625 + $6.875 (X) Chapter 3-17 Hansen, Mowen, Elias & Senkow (ITP, 1998) Utility Cost Scatterplot Method $8,000 Important: Cost function is only . relevant within relevant range 6,000 . 4,000 . Analyst can fit line . based on his or her experience 2,000 . 0 200 400 600 800 1,000 Units Produced Chapter 3-18 Hansen, Mowen, Elias & Senkow (ITP, 1998) The Method of Least Squares X Y XY X 2 Y 2 200 $2,000 400,000 40,000 $4,000,000 400 2,500 1,000,000 160,000 6,250,000 600 4,500 2,700,000 360,000 20,250,000 800 5,000 4,000,000 640,000 25,000,000 1,000 7,500 7,500,000 1,000,000 56,250,000 3,000 $21,500 $15,600,000 2,200,000 $117,750,000 V = [ XY - X Y/n]/[ X2 - ( X)2/n] = 2,700,000/400,000 = $6.75 The cost formula is: F = Y/n-V X/n = $21,500/5 - [$6.75(3,000/5)] Y = $250 + $6.75 (X) = $250 Chapter 3-19 Hansen, Mowen, Elias & Senkow (ITP, 1998) The Method of Least Squares: Goodness of Fit R2 (Coefficient of Determination) = V[ XY- X Y/n]/[ Y2- ( Y)2/n] R2 = .944 R (Coefficient of Correlation) = Square root of R2 = .972 Chapter 3-20 Hansen, Mowen, Elias & Senkow (ITP, 1998) Product Complexity and Multiple Drivers TC = FC +V1C1 + V2C2 Recommended Use of Multiple Regression Chapter 3-21 Hansen, Mowen, Elias & Senkow (ITP, 1998) Cost Behaviour and Managerial Judgement Some Tips Use past experience Try to confirm results with operating personnel Use common sense to confirm statistical studies Chapter 3-22 Hansen, Mowen, Elias & Senkow (ITP, 1998) Numerical Questions from back of chapters 2 and 3 W2-3, E2-9, P2-1, P2-9 W3-3, E3-9, P3-1 Chapter 3-23 Hansen, Mowen, Elias & Senkow (ITP, 1998) Question W2-3 Please go to your text to read this question. Chapter 3-24 Hansen, Mowen, Elias & Senkow (ITP, 1998) Question E2-9 Please go to your text to read this question. Chapter 3-25 Hansen, Mowen, Elias & Senkow (ITP, 1998) Question P2-1 Please go to your text to read this question. Chapter 3-26 Hansen, Mowen, Elias & Senkow (ITP, 1998) Question P2-9 Please go to your text to read this question. Chapter 3-27 Hansen, Mowen, Elias & Senkow (ITP, 1998) Question W3-3 Please go to your text to read this question. Chapter 3-28 Hansen, Mowen, Elias & Senkow (ITP, 1998) Question E3-9 Please go to your text to read this question. Chapter 3-29 Hansen, Mowen, Elias & Senkow (ITP, 1998) Question P3-1 Please go to your text to read this question. Chapter 3-30 Hansen, Mowen, Elias & Senkow (ITP, 1998) The End Chapter 3-31

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